On a system of nonlinear Schrödinger equations with quadratic interaction

Nakao Hayashi*, Tohru Ozawa, Kazunaga Tanaka

*この研究の対応する著者

研究成果: Article査読

44 被引用数 (Scopus)

抄録

We study a system of nonlinear Schrödinger equations with quadratic interaction in space dimension n≤6. The Cauchy problem is studied in L 2, in H1, and in the weighted L2 space 〈 x〉-1L2=F(H1) under mass resonance condition, where 〈x〉=( 1+|x|2)1/2 and F is the Fourier transform. The existence of ground states is studied by variational methods. Blow-up solutions are presented in an explicit form in terms of ground states under mass resonance condition, which ensures the invariance of the system under pseudo-conformal transformations.

本文言語English
ページ(範囲)661-690
ページ数30
ジャーナルAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
30
4
DOI
出版ステータスPublished - 2013

ASJC Scopus subject areas

  • 分析
  • 数理物理学
  • 応用数学

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